Synthesis of light beams

Abstract

A method and system for synthesizing a desired light beam including calculating a two-dimensional light filter for an optical element, the two-dimensional light filter being such that the optical element produces under free space propagation, in response to illumination thereof, a three-dimensional light distribution that approximates the light distribution of the desired light beam, and illuminating the optical element.

What is claimed is:  
     
       1. A method for synthesizing a desired light beam comprising: 
       calculating a two-dimensional light filter for an optical element, the two-dimensional light filter being such that the optical element produces under free space propagation, in response to illumination thereof, a three-dimensional light distribution that approximates the light distribution of the desired light beam; and  
       illuminating the optical element.  
     
     
       2. The method of  claim 1  wherein the desired light beam is an elongated focused beam. 
     
     
       3. The method of  claim 1  wherein the optical element is a diffractive element. 
     
     
       4. The method of  claim 1  wherein the optical element is a micro-optical element. 
     
     
       5. The method of  claim 1  wherein the optical element uses mirrors to filter incoming light. 
     
     
       6. The method of  claim 1  wherein the optical element is a refractive element. 
     
     
       7. The method of  claim 1  wherein the two-dimensional light filter is a phase-only filter. 
     
     
       8. The method of  claim 1  wherein the two-dimensional light filter is an amplitude-only filter. 
     
     
       9. The method of  claim 1  wherein the two-dimensional light filter is such that the optical element produces under free space propagation, in response to illumination thereof, a three-dimensional light distribution that best approximates the light distribution of the desired light beam with respect to a prescribed error metric, as compared with three-dimensional light distributions produced by other two-dimensional light filters. 
     
     
       10. The method of  claim 9  wherein the prescribed error metric is a least squares metric. 
     
     
       11. The method of  claim 1  wherein the convolution of the two-dimensional light filter for the optical element with a free space propagation impulse response function approximates the light distribution of the desired light beam. 
     
     
       12. The method of  claim 11  wherein the convolution of the two-dimensional light filter for the optical element with a free space propagation impulse response function best approximates the light distribution of the desired light beam with respect to a prescribed error metric, as compared with other two-dimensional light filters. 
     
     
       13. The method of  claim 12  wherein the prescribed error metric is a least squares metric. 
     
     
       14. The method of  claim 1  wherein said calculating step includes solving a linear integral equation. 
     
     
       15. The method of  claim 1  wherein said calculating step uses Fourier transforms to calculate the two-dimensional light filter. 
     
     
       16. The method of  claim 1  wherein said calculating step is performed analytically. 
     
     
       17. The method of  claim 1  wherein said calculating step is performed by a computer. 
     
     
       18. The method of  claim 1  wherein said calculating step comprises: 
       choosing a candidate two-dimensional light filter for an optical element situated in a reference plane;  
       deriving a plurality of forward planar light distributions within a respective plurality of transverse planes parallel to the reference plane, by applying forward free space propagation to an incoming light wave transverse to the optical element;  
       modifying the plurality of forward planar light distributions;  
       further deriving a plurality of back-propagated planar light distributions by applying backward free space propagation to each of the plurality of modified forward planar light distributions; and  
       producing a modified candidate two-dimensional light filter by taking an average of the plurality of back-propagated planar light distributions.  
     
     
       19. The method of  claim 18  wherein the desired light beam is an elongated focused light beam. 
     
     
       20. The method of  claim 18  wherein the optical element is a diffractive element. 
     
     
       21. The method of  claim 18  wherein the optical element is a micro-optical element. 
     
     
       22. The method of  claim 18  wherein the optical element uses mirrors to filter incoming light. 
     
     
       23. The method of  claim 18  wherein the optical element is a refractive element. 
     
     
       24. The method of  claim 18  wherein the desired light beam is specified by constraints at the plurality of transverse planes, and wherein said modifying step at least partially applies the constraints. 
     
     
       25. The method of  claim 24  wherein the constraints are constraints on the intensities of light distributions at the plurality of transverse planes. 
     
     
       26. The method of  claim 18  wherein the two-dimensional light filter is a phase-only filter. 
     
     
       27. The method of  claim 18  wherein the two-dimensional light filter is an amplitude-only filter. 
     
     
       28. The method of  claim 18  wherein said modifying step modifies intensities of the forward planar light distributions without modifying phases of the forward planar light distributions. 
     
     
       29. The method of  claim 18  wherein said modifying step modifies the forward planar light distributions at spatial locations within a prescribed set of locations. 
     
     
       30. The method of  claim 18  wherein the average of the plurality of back-propagated planar light distributions is a weighted average of the plurality of back-propagated planar light distributions. 
     
     
       31. The method of  claim 18  wherein said deriving, modifying, further deriving and producing steps are repeated at least once. 
     
     
       32. The method of  claim 18  wherein said deriving, modifying, further deriving and producing steps are repeated a prescribed number of times. 
     
     
       33. The method of  claim 18  wherein said deriving, modifying, further deriving and producing steps are repeated until the modified candidate two-dimensional light filters produced at each repetition satisfy a prescribed convergence criterion. 
     
     
       34. The method of  claim 1  wherein said illuminating step illuminates the optical element by a planar light wave transverse thereto. 
     
     
       35. A method for synthesizing a desired light beam comprising: 
       calculating a plurality of phase-only light filters for a respective plurality of optical elements, the plurality of phase-only light filters being such that the plurality of optical elements when mounted in series produce under free space propagation, in response to illumination thereof, a three-dimensional light distribution that approximates the light distribution of the desired light beam; and  
       illuminating the plurality of optical elements.  
     
     
       36. The method of  claim 35  wherein the desired light beam is an elongated focused light beam. 
     
     
       37. The method of  claim 35  wherein said calculating step applies an algorithm of Gerchberg-Saxton in a Fresnel domain. 
     
     
       38. A system for synthesizing a desired light beam comprising: 
       a processor calculating a two-dimensional light filter for an optical element, the two-dimensional light filter being such that the optical element produces under free space propagation, in response to illumination thereof, a three-dimensional light distribution that approximates the light distribution of the desired light beam; and  
       an optical element filtering incoming light according to the two-dimensional light filter.  
     
     
       39. The system of  claim 38  wherein the desired light beam is an elongated focused light beam. 
     
     
       40. The system of  claim 38  wherein said optical element is a diffractive element. 
     
     
       41. The system of  claim 38  wherein said optical element is a micro-optical element. 
     
     
       42. The system of  claim 38  wherein said optical element uses mirrors to filter incoming light. 
     
     
       43. The system of  claim 38  wherein said optical element is a refractive element. 
     
     
       44. The system of  claim 38  wherein the two-dimensional light filter is a phase-only filter. 
     
     
       45. The system of  claim 38  wherein the two-dimensional light filter is an amplitude-only filter. 
     
     
       46. The system of  claim 38  wherein the two-dimensional light filter is such that said optical element produces under free space propagation, in response to illumination thereof, a light distribution that best approximates the light distribution of the desired light beam with respect to a prescribed error metric, as compared with three-dimensional light distributions corresponding to other two-dimensional light filters. 
     
     
       47. The system of  claim 38  wherein said processor comprises: 
       a free space propagation unit applying forward free space propagation to an incoming light wave transverse to an optical element situated in a reference plane, producing a plurality of forward planar light distributions within a respective plurality of transverse planes parallel to the reference plane, and applying backward free space propagation to modified forward planar light distributions, producing a plurality of back-propagated planar light distributions;  
       a modification unit modifying the plurality of forward planar light distributions, producing the modified forward planar light distributions; and  
       an averaging unit generating an average of the plurality of back-propagated planar light distributions.  
     
     
       48. The system of  claim 47  wherein the desired light beam is specified by constraints at the plurality of transverse planes, and wherein said modifying step at least partially applies the constraints. 
     
     
       49. The system of  claim 48  wherein the constraints are constraints on the intensities of light distributions at the plurality of transverse planes. 
     
     
       50. The system of  claim 47  wherein said modification unit is operational to modify intensities of the plurality of forward planar light distributions, without modifying phases of the plurality of forward planar light distributions. 
     
     
       51. The system of  claim 47  wherein said modification unit is operational to modify the plurality of forward planar light distributions at spatial locations within a prescribed set of locations. 
     
     
       52. The system of  claim 47  wherein said averaging unit generates a weighted average of the plurality of back-propagated planar light distributions. 
     
     
       53. A system for synthesizing a desired light beam comprising: 
       a processor calculating a two-dimensional light filter for an optical element, the two-dimensional light filter being such that the optical element produces under free space propagation, in response to illumination thereof, a three-dimensional light distribution that approximates the light distribution of the desired light beam; and  
       a plurality of optical elements with phase-only light filters mounted in series which, when used in combination, filter incoming light according to the two-dimensional light filter.  
     
     
       54. The system of  claim 53  wherein the desired light beam is an elongated focused light beam. 
     
     
       55. An elongated focused light beam for use within an optical scanner, made by the process of: 
       calculating a two-dimensional light filter for an optical element, the two-dimensional light filter being such that the optical element produces under free space propagation, in response to illumination thereof, a three-dimensional light distribution that approximates the light distribution of a desired light beam; and  
       illuminating the optical element.  
     
     
       56. An elongated focused light beam for use within an optical scanner, made by the process of: 
       calculating a plurality of phase-only light filters for a respective plurality of optical elements, the plurality of phase-only light filters being such that the plurality of optical elements when mounted in series produce under free space propagation, in response to illumination thereof, a three-dimensional light distribution that approximates the light distribution of a desired light beam; and  
       illuminating the plurality of optical elements.  
     
     
       57. An article of manufacture including one or more computer readable media that embody a program of instructions for synthesizing a desired light beam, wherein the program of instructions, when executed by a processor, causes the processor to calculate a two-dimensional light filter for an optical element, the two-dimensional light filter being such that the optical element produces under free space propagation, in response to illumination thereof, a three-dimensional light distribution that approximates the light distribution of the desired light beam. 
     
     
       58. The article of manufacture of  claim 57  wherein the one or more computer readable media include one or more non-volatile storage devices. 
     
     
       59. The article of manufacture of  claim 57  wherein the one or more computer readable media include a carrier wave modulated with a data signal.